A057474 Numbers k such that x^k + x^5 + 1 is irreducible over GF(2).

2, 3, 6, 9, 12, 14, 17, 20, 23, 44, 47, 63, 84, 129, 236, 278, 279, 297, 300, 647, 726, 737, 2574, 2660, 4233, 4500, 8207, 11900, 16046, 21983, 23999, 24596, 24849, 84929, 130926, 156308, 160046, 185142, 270641

Offset

1,1

Comments

Next term is > 10^5. - Joerg Arndt, Apr 28 2012

Next term is > 241000. - Manfred Scheucher, Aug 18 2015

Any subsequent terms are > 300000. - Lucas A. Brown, Nov 28 2022

Links

Table of n, a(n) for n=1..39.

Joerg Arndt, Matters Computational (The Fxtbook), section 40.9.3 "Irreducible trinomials of the form 1 + x^k + x^d", p.850

Lucas A. Brown, Python program.

Lucas A. Brown, Sage program.

Prog

(Sage)
P.<x> = GF(2)[]
for n in range(10^4):
    if (x^n+x^5+1).is_irreducible():
        print(n) # Joerg Arndt, Apr 28 2012

Crossrefs

Cf. A002475.

Sequence in context: A191981 A131975 A288754 * A347785 A373698 A270139

Adjacent sequences: A057471 A057472 A057473 * A057475 A057476 A057477

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Sep 27 2000

Extensions

a(23)-a(34) by Joerg Arndt, Apr 28 2012

a(35)-a(38) by Manfred Scheucher, Aug 18 2015

a(39) from Lucas A. Brown, Nov 28 2022

Status

approved